THE LAG STRUCTURE OF THE RELATIONSHIP BETWEEN PATENTING AND INTERNAL R&D REVISITED

Ning WangDepartment of Organization and Strategy

Maastricht UniversityThe Netherlands

Tel (31) 43-3884793Fax (31) 43-3884893

N.Wang@maastrichtuniversity.nl

John HagedoornDepartment of Organization and Strategy and UNU-MERIT

Maastricht UniversityThe Netherlands

Tel (31) 43-3883823Fax (31) 43-3884893

&Department of Management

Royal Holloway, University of LondonEgham, Surrey

United KingdomJ.Hagedoorn@maastrichtuniversity.nl

8 Apr, 2013 First Version13 Nov, 2013 Revised

Research Policy

The Lag Structure of the Relationship between Patenting and Internal R&D Revisited

Abstract

The principal purpose of this study is to revisit the classic research question of the lag structure of the patents-R&D relationship through an examination of the impact of internal R&D on firm patenting in the context of the global pharmaceutical industry during 1986–2000. Our empirical analysis, using both a multiplicative distributed lag model and a dynamic linear feedback model, differs from previous work that examines the patents-R&D relationship in three aspects. First, our estimation results exhibit direct evidence on lagged R&D effects, with the first lag (t-1) of R&D being significant in all distributed lag specifications. Second, a U-shaped lag structure of the patents-R&D relationship is found in most estimations of the multiplicative distributed lag model, which suggests a potential long-run effect of internal R&D investments on firm patenting. Finally, the results from the dynamic linear feedback model coincide with those from the multiplicative distributed lag model, indicating not only lag effects from recent R&D investments but also an overall long-run effect of internal R&D investments in the distant past on the knowledge production or innovation process of incumbent pharmaceutical firms.

Keywords: Patents; Internal R&D; Lag Structure; Multiplicative Distributed Lag Model; Dynamic Linear Feedback Model; Pharmaceutical Industry

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1. INTRODUCTION

In the attempt to learn about gestation lags in knowledge production of in-house research

and development (R&D) by firms, researchers have repeatedly examined the relationship

between R&D expenditures and patents, which are taken as an output indicator of R&D

(Bound et al., 1984; Griliches, 1990)1. The question of interest is the lag structure of the

patents-R&D relationship, studied by considering the number of patents applied for and

granted to firms as a function of their current and lagged R&D expenditures. Pakes and

Griliches (1984a) is probably the first attempt to look at the time shape of the distributed

lag between patenting and internal R&D activity of firms. In their panel-data model (with

a log-log functional form), Pakes and Griliches (1984a) found evidence of a lag

truncation effect in the distributed lag of R&D on patents. The estimated coefficient on

the last lag of R&D, with five lagged R&D terms in their model, was significantly higher

than the coefficients of more recent R&D2.

Hausman et al. (1984) and Hall et al. (1986) analyzed the same research question

whether there is a lag in the relationship between patenting and R&D expenditures. Using

a more appropriate functional form that reflected explicitly the non-negativity and

discreteness of patent counts in the context of panel data, Hausman et al. (1984) found a

U-shaped lag structure in the random-effects estimation but not in their conditional fixed-

1 Internal R&D is usually measured as annual R&D expenditures by firms. A related question is to what extent patents serve as a good indicator of the output of R&D. Patents are directly related to inventiveness and represent an externally validated measure of technological novelty (Griliches, 1990). However, the use of patents as an economic indicator of knowledge increments has some limitations. For instance, not all inventions are patentable or patented, and the inventions that are patented differ greatly in their economic significance (Bound et al., 1984; Griliches, 1990; Pakes and Griliches, 1984a).2 The coefficient of the fifth year could be proxying for a series of small effects of the more basic research done six years ago or earlier, thus suggesting a lag “truncation” effect (Pakes and Griliches, 1984a). See Pakes and Griliches (1984b) for further discussion of this issue.

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effects version. When they conditioned their estimates on the total number of patents

received by a firm over the observed years, no coefficients except for the

contemporaneous R&D were statistically significant either in the Poisson or negative

binomial model. Hall et al. (1986) found similar results and concluded that there was

very little direct evidence of anything but simultaneity in the year-to-year movement of

patents and R&D expenditures, though an indirect analysis performed in their study

suggested a possible distributed lag structure.

The consistency of the previously described panel-data models3 rests on the

assumption that patents are an indicator of the output or ‘success’ of R&D rather than the

input of R&D (Hall et al., 1986). However, as the patent application tends to occur

relatively early in the life of a research project and the bulk of R&D expenditures often

occur after the application is made, new patents virtually generate the need for future

R&D expenditures (Griliches, 1990; Hall et al., 1986). Therefore, R&D expenditures

should be seen as a predetermined variable instead of a strictly exogenous one. Such

concern in the relationship of patents to internal R&D activity was first addressed by Hall

et al. (1986) using a simple version of a Granger causality test, with a view to testing if

past success in patenting leads to an increase in a firm’s future R&D investments4.

Montalvo (1997) applied a quasi-differenced generalized method of moments (GMM)

estimator to the analysis of the patents-R&D relationship so as to obtain consistent 3 See Guo and Trivedi (2002) for a cross section analysis of the patents-R&D relationship. Their estimation results were in line with Hall et al. (1986).4 Following Hall et al. (1986), a Granger causality test was performed in this study as well (see the results shown in Appendix A–Table A1). The current level of Log R&D was predicted with two lags of Log R&D (based on an approximate AR (2) specification) as well as contemporaneous and lagged Log Patents. As shown from column (6) through (10), the estimated coefficient on contemporaneous Log Patents was significant, but lagged Log Patents were of no help in predicting future R&D. The same behavioral pattern of lagged Log Patents was identified even when contemporaneous Log Patents was left out of the equation in columns (11)–(14). Thus, there was no evidence suggesting that past success in patenting led to an increase in a firm’s future R&D investments above and beyond that implied by its R&D history.

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estimates in the presence of predetermined regressors, i.e., R&D expenditures5. The

results turned out to be somewhat inconclusive as well: the estimated coefficient on

contemporaneous R&D was not statistically significant while the first lag of R&D had a

significant effect on patents.

Blundell et al. (2002) extended the quasi-differenced GMM estimation with an

application to a dynamic linear feedback model and proposed an alternative estimator, the

pre-sample mean (PSM) estimator, based upon pre-sample information on the dependent

variable. In their application to the analysis of the patents-R&D relationship, the results

for the dynamic linear feedback model from the PSM estimator indicated a much lower

depreciation rate of internal R&D investments—a potential long-run effect of in-house

R&D on firm patenting—than that implied by the results from the multiplicative

distributed lag model in prior literature. A recent study on the patents-R&D relationship

by Gurmu and Pérez-Sebastián (2008) reported lagged R&D effects that were moderately

higher than those previously found, but the lag effects on patents were identified only for

more recent R&D.

So far the earlier work in this area, as aforementioned, has investigated the

relationship between patenting and internal R&D activity of firms for the U.S.

manufacturing sector during the 1970’s (Blundell et al., 2002; Hall et al., 1986; Hausman

et al., 1984; Montalvo, 1997; Pakes and Griliches, 1984a) and over the 1980’s (Gurmu

and Pérez-Sebastián, 2008). Our study aims to revisit this classic research question

regarding the lag structure of the patents-R&D relationship by applying recently

5 Chamberlain (1992) and Wooldridge (1997) developed a quasi-differenced GMM estimator that is consistent for count panel data models with predetermined regressors. This quasi-differenced GMM estimator has been applied to the analysis of the patents-R&D relationship by Montalvo (1997), Crépon and Duguet (1997), Cincera (1997), and Gurrmu and Pérez-Sebastián (2008).

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developed estimation techniques on firm-level panel data for the global pharmaceutical

industry from 1986 to 2000. Prior research suggests that the relationship between

patenting and internal R&D activity of firms differs across industries (Griliches, 1990;

Hall et al., 1986). We attempt to address this concern by taking a closer look at the lag

structure of the patents-R&D relationship within one industry. We focus on the global

pharmaceutical industry for two main reasons. First, the pharmaceutical industry as a

high-technology sector is characterized by high-levels of patenting propensity and R&D

intensity. Previous studies demonstrate that patenting activity is an important source of

technological advantage in the pharmaceutical industry (Henderson and Cockburn, 1994;

Levin et al., 1987). In addition, recent figures show that pharmaceutical firms invest as

much as five times more in R&D, relative to their sales, than the average U.S.

manufacturing firm (CBO Study, 2006)6. Second, empirical evidence clearly indicates

that the proportion of research (‘R’) in R&D expenditures is the main contributor to

patents, whereas the bulk of development (‘D’) costs lead more to products and processes

(Czarnitzki et al., 2009)7. Given that the ‘D’ part of R&D expenditures, relative to ‘R’, is

mostly the larger one, the estimated patents-R&D elasticity would be biased downwards

when development costs are of minor relevance for patent production (Czarnitzki et al.,

2009; Griliches, 1990). As the pharmaceutical industry is actually among the most

research-intensive sectors with a very large share of ‘R’ (CBO Study, 2006), studying the

6 A CBO Study: Research and Development in the Pharmaceutical Industry, Publication No. 2589, Congressional Budget Office, October 2006, available at http://www.cbo.gov/ftpdocs/76xx/doc7615/10-02-DrugR-D.pdf. 7 Using Flemish R&D Survey data, Czarnitzki et al. (2009) provided empirical evidence on the differential contribution of research (‘R’) and development (‘D’) to patents and identified a high premium of research (‘R’), relative to overall R&D, towards firm patenting.

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pharmaceutical industry may alleviate the above-mentioned problem that the ‘relevant’

R&D is measured with error (Griliches, 1990) in the patents-R&D relationship.

Our empirical analysis, using both a multiplicative distributed lag model and a

dynamic linear feedback model, differs from previous work that examines the patents-

R&D relationship in three aspects. First, our estimation results exhibit direct evidence on

lagged R&D effects, with the first lag (t-1) of R&D being significant in all distributed lag

specifications. Evidence for the contribution of the first lag of R&D to the current year’s

patent counts is of more than 25% of the total R&D elasticity. Second, a U-shaped lag

structure of the patents-R&D relationship is found in most estimations of the

multiplicative distributed lag model. This finding suggests a potential long-run effect of

internal R&D investments on firm patenting. Finally, the estimation results from the

dynamic linear feedback model coincide with those from the multiplicative distributed

lag model, indicating not only lag effects from recent R&D investments but also an

overall long-run effect of internal R&D investments in the distant past in the knowledge

production or innovation process of incumbent pharmaceutical firms.

The rest of this paper is structured as follows. In section 2, we provide the

theoretical background to the expected lag effects of internal R&D investments by firms,

lags effects that may last during the long run of the knowledge production or innovation

process. In that section, we also formulate our main hypothesis. Section 3 describes the

derivation of the data set and looks at the properties of the various variables. Section 4

proceeds by presenting the two count panel data models underlying our empirical

analysis—the multiplicative distributed lag model and the dynamic linear feedback model

—and their associated estimation techniques. The empirical results are then reported in

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Section 5. Section 6 summarizes our main results and their implications and it discusses

some possible future lines of work.

2. THEORETICAL BACKGROUND AND HYPOTHESIS

Knowledge production or innovation is often described as a recombinant process that

involves combining existing bits of knowledge in the creation of new knowledge

(Fleming, 2001; Kogut and Zander, 1992). A firm’s existing bits of knowledge or

knowledge stock is built up over time through its previous investments in R&D (Hall et

al., 1986). In the context of the relationship between patents and R&D expenditures, the

annual R&D expenditures are considered to be investments which add to a firm’s

knowledge stock, and patents are taken as an output indicator of new knowledge creation

or innovation (Hall et al., 1986; Hausman et al., 1984). As argued by Scotchmer (1991),

the innovation process is of a cumulative nature such that early innovations (i.e.,

knowledge stock) provide a boost or a technological foundation for later innovations (i.e.,

new knowledge)8. This forms a theoretical rationale underlying the lag effects of R&D

investments in the sense of contributions to firm innovativeness.

A firm’s knowledge stock usually depreciates as time passes (Hall et al., 1986)

since knowledge tends to become obsolete and it no longer matches the demands of its

current environment (Eisenhardt, 1989; Helfat and Raubitschek, 2000). In this respect,

more recently created knowledge is often considered more valuable for knowledge

production or innovation because of organization-environment fit (Sørensen and Stuart,

2000), capability building in emerging areas (McGrath, 1999), temporal local search

8 We are thankful to an anonymous referee’s valuable advice on this point.7

(Helfat, 1994; Martin and Mitchell, 1998), and cognitive and institutional pressures

(Martins and Kambil, 1999; Nerkar, 2003). In other words, in the case of the patents-

R&D relationship, recent R&D investments are expected to have a greater impact on firm

patenting, while the contribution of older R&D has become less valuable with the

passage of time.

However, research also suggests that recent knowledge may not necessarily be

representative of the technologically superior or optimal solution that has emerged

(Abrahamson, 1996). In contrast, a firm’s older knowledge spread across long time spans,

accruing from its R&D investments in the distant past, may also be influential with

respect to new knowledge creation or innovation (Garud and Nayyar, 1994; Nerkar,

2003). For example, incumbent pharmaceutical firms often review their previously

discarded experimental compounds, some of which failed in clinical trials as long as

twenty years ago, hoping that an old compound intended for one treatment may be useful

in treating something different nowadays (Simons, 2006). The rationale for the important

role of older knowledge is that it is characterized by increased reliability and legitimacy,

as older knowledge is usually better tested and understood by firms than recently created

knowledge, thereby decreasing the chances of costly errors and increasing the likelihood

of successful innovation (Katila, 2002; March, 1991). The far-reaching influence of older

knowledge implies that even long past R&D investments by firms can still play a crucial

part in their knowledge production or innovation, or put differently, the lag effects

produced by internal R&D investments may last over a long time horizon.

Such potential long-run effect of in-house R&D is consistent with a real options

logic for managing R&D investment strategies of firms. As stated by Myers (1984) “ …

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the value of R&D is almost all option value …”. R&D investments can be considered to

be real options that convey the right for firms to preserve their decision rights in the

future in their investment choices (Garud and Nayyar, 1994; McGrath, 1997). Comment

JH: similar sentence appears two sentences further down. For firms operating in a rapidly

changing environment, it is important to constantly direct their R&D efforts towards new

technological areas that are often characterized by high levels of technical uncertainty.9 In

the face of technical uncertainty, it is in the best interests of firms to invest immediately,

otherwise they might be subject to a discounting penalty or even the risk of lock-out

(McGrath, 1997). Such investments in R&D are viewed as real options that create value

by providing firms with the luxury of waiting and watching as more information about

uncertainty is revealed (McGrath, 1997; Nerkar, 2003). Specifically, some knowledge

derived from past R&D investments may demonstrate a great potential value at a future

date when conditions favor its (re)use, for instance, through coevolution of

complementary knowledge, markets, institutions, or standards that are necessary for

employing useful but untapped knowledge (Garud and Nayyar, 1994; Nerkar, 2003). To

the extent that it might take a very long time for these favorable conditions to emerge,

there are time lags for firms’ past knowledge to become conducive for future knowledge

creation or innovation. Furthermore, in addition to waiting and watching after the initial

investment in R&D, i.e., the opened option, firms may have strong incentives to persist in

making investments in the same area (McGrath and Nerkar, 2004). This is due to

increases in absorptive capacity that, with the cumulative experience through previous

9 Technical uncertainty refers to the likely costs and probabilities of accomplishing technical success. This form of uncertainty can only be reduced through investment by firms. Such technical uncertainty creates pressure on firms to invest immediately (Dixit and Pindyck, 1994; McGrath, 1997).

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track record of investments, makes the assimilation of subsequent knowledge in the same

area easier, faster, and less expensive (Cohen and Levinthal, 1990; McGrath and Nerkar,

2004). Such sequential investing in internal R&D leads to a cumulative, path-dependent

knowledge production or innovation process, which makes the very early option

investments in R&D valuable or even vital for a firm’s success in a new technological

area. Hence, from the perspective of real options reasoning, early R&D investments by

firms may generate a long-lasting impact on future knowledge creation or innovation.

The above indicates that a firm’s internal R&D investments give rise to, not only

lag effects in the short run that arise from more recent R&D, but also a potential long-run

effect resulting from its distant R&D history in the knowledge production or innovation

process. We therefore propose the following main hypothesis:

Hypothesis: Taking patents as an output indicator of firms’ innovativeness, lag effects

of firms’ internal R&D investments are expected to impact their long run knowledge

production or innovation process.

3. DATA AND VARIABLE CONSTRUCTION

The research setting for this study is the global pharmaceutical industry, which is on the

verge of profound mutations as a new biotechnology-based technological regime has

emerged. More in particular, we will focus on incumbent pharmaceutical firms which

attempt to build up innovative capabilities within this new technological regime.

Incumbent pharmaceuticals are defined as pharmaceutical firms that were in existence

prior to the emergence of biotechnology. These companies, such as Bayer, Hoffmann-La

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Roche, Merck, and Pfizer, are generally mature and very large firms that dominated the

industry since the 1940s. In the mid-1970s, new biotechnology brought along significant

scientific and technological breakthroughs in genetic engineering (recombinant DNA,

1973) and hybridization (monoclonal antibodies, 1975). These advances virtually serve as

a radical process innovation for incumbent pharmaceutical companies in the way new

drugs are discovered and developed (Pisano, 1997).

To mitigate a potential survivor bias, we started with a comprehensive set of

incumbent pharmaceutical firms alive as of 1986 based on various industry sources10.

Through this process, we identified 89 incumbent pharmaceutical firms, defined as

pharmaceutical firms that were founded prior to the emergence of biotechnology in the

mid-1970s. A further scrutiny criterion for the sample firms is based on the absence of

large jumps during the time period of 1986–2000. Following Hall et al. (1986), a jump is

defined as an increase in total assets or employment of more than 100 per cent or a

decrease of more than 50 per cent11. This test was not applied unless the change in total

assets was greater than two million dollars or the change in employment was greater than

500 employees. Our study ultimately ended up with a slightly unbalanced panel sample

of 85 firms covering the 15-year period from 1986 to 2000, giving 1,186 firm-year

observations.

An important source of data for our study is the Technology Profile Report

maintained by the U.S. Patent and Trademark Office (USPTO). All patent data used in

this study are based on successful patent applications, or granted patents. The application

10 The sample for this study was drawn by referring to Compustat, Datastream, Amadeus, SIC reports, Ernst and Young’s Annual Biotech Industry Reports, Scrip’s Pharmaceutical Yearbook, amongst others.11 For the sample firms in our study, total assets are a better indicator of scale change than capital stock, which was used in Hall et al. (1986).

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date of a patent is only reported when the patent is actually granted. On average it may

take three years for the USPTO to grant a patent after it was originally applied for by an

inventing firm (Biotechnology Industry Organization, 2008). In contrast, there is

essentially no lag time between the completed invention and the patent application date,

which is on average no more than three months (Darby and Zucker, 2003). Thus, the

application date of a granted patent is closely tied to the timing of the new knowledge

creation and should be used as the relevant time placer for patents (Hall et al., 2001;

Trajtenberg, 1990). Accordingly, we assigned a granted patent to the year in which the

patent was originally applied for. For instance, a patent applied for in 1986 but granted in

1989 is considered a 1986 patent. We use USPTO patent data for both US and non-US

firms. Although US patent data could imply a bias against non-US firms, it is mentioned

in the literature that, given the importance of the US market, the patent protection offered

by US authorities, and the level of technological sophistication of the US market, it is

inevitable that non-US firms, in particular leading, large firms file their patents in the

USA (Hagedoorn and Cloodt, 2003; Patel and Pavitt, 1991). Furthermore, as suggested

by Ahuja and Katila (2001), to maintain a certain level of consistency, reliability and

comparability choosing one patenting system is preferred to using several patenting

systems across nations.

Financial figures and employment data were obtained from Compustat and

Datastream (Thomson Financial). For all firms, financial data were converted to U.S.

dollars and are inflation-adjusted in millions of year 2000 dollars.

Dependent Variable

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The dependent variable for this study is the number of patents applied for by an

incumbent pharmaceutical firm in a given year that are eventually granted, which is taken

as an output indicator of advances in knowledge, or more in general, firm innovativeness.

As displayed in Table 1, the frequency distribution of the number of patents is

characterized by heavy upper tails with a range of 0 to 800, a mean value of about 94, and

a relatively low median value of 45. The first and third quantile values are 14 and 116

patents, respectively. Over the whole study period, the proportion of zero patents is only

1%, while the fraction with at least 100 patents is 29%. Compared to previous studies

(See e.g., Cincera, 1997; Gurmu and Pérez-Sebastián, 2008; Hall et al., 1986; Hausman

et al., 1984), the variance of the number of patents is slightly larger than the mean,

indicating the presence of a moderate overdispersion in our patent data12.

Insert Table 1 here

Independent Variable

The main explanatory variables of interest are the natural logarithms of current and

lagged values of internal R&D investments. We measured an incumbent pharmaceutical

firm’s internal R&D investments by its annual R&D expenditures. The annual R&D

expenditures are considered to be investments that add to a firm’s stock of knowledge,

whose value decays over time such that the contribution of older R&D investment

becomes less valuable as time passes (Hall et al., 1986). Table 1 shows that incumbent

pharmaceuticals are R&D-intensive firms, their average R&D expenditures amounting to

12 See Guo and Trivedi (2002), Gurrmu and Pérez-Sebastián (2008) for the flexible techniques that are more desirable for highly overdispersed data.

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approximately 505 million dollars per year. From Table 2 we can see that R&D

expenditures by incumbent pharmaceutical firms are highly correlated over time, with the

first order autocorrelation of about 0.99 and the correlation among R&D regressors all

above 0.95. We will discuss this issue of a highly persistent R&D series at greater length

in the forthcoming sections. R&D expenditures are inflation-adjusted in millions of year

2000 dollars.

Insert Table 2 here

Control Variables

The logarithm of pre-sample mean of patents is included to proxy for the unobserved

heterogeneity in firm knowledge production (Blundell et al., 1995; Blundell et al., 2002).

We used the average number of patents by a pharmaceutical firm in the period from 1981

to 1985, i.e., a five-year period of pre-sample history, to construct the pre-sample mean

variable.

Following previous studies (Gurmu and Pérez-Sebastián, 2008; Hall et al., 1986;

Hausman et al., 1984), we used a time-constant regressor, i.e., the logarithm of book

value of equity in year 2000 in millions of dollars, as a measure for firm size13. For those

firms that fail to survive till year 2000, the end year value of equity is used and inflation-

adjusted.

13 We also used the logarithm of the annual values of equity to control for firm size. A one-year lag of this variable is included in all the model estimations. Since a few firm-year values of equity are negative, we changed the negative value into 0.000001 (million dollars) before taking the logarithms. The estimated results are basically similar.

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To control for country-specific institutional configurations that are significant in

shaping firms’ propensities to patent (Jaffe and Trajtenberg, 1999), we included two

indicator variables based upon the location of company headquarters. One indicator

variable is coded as 1 if a pharmaceutical firm is located in the United States (1 = U.S.

Firm), and the other indicator is coded as 1 if a pharmaceutical firm is headquartered in

Europe (1 = European Firm), with a Japanese location as the reference category. The

global nature of our data set is reflected in the fact that 33% of the firms are U.S. based,

30% are European based, with the remaining 37% headquartered in Japan.

In contrast to previous studies (Hall et al., 1986; Hausman et al., 1984; Gurmu and

Pérez-Sebastián, 2008) where a scientific sector dummy was used to distinguish R&D-

intensive industries from other manufacturing industries, our study focuses on one high-

tech industry in the scientific sector, the global pharmaceutical industry. Since the

pharmaceutical industry is made up of both specialized pharmaceutical firms and more

diversified, mainly chemical, conglomerates, we controlled for a pharmaceutical firm’s

degree of diversification by coding the firm as 1 if it is a specialized company (1 =

Pharma Firm) and 0 otherwise. Specialized pharmaceutical firms are those active in SIC

2834 (Pharmaceutical Preparations Manufacturing), whereas a conglomerate might

engage, for instance, in both SIC 2834 and SIC 2890 (Chemical Products

Manufacturing). About one half of the firms in the sample are fully specialized (46%).

Over time, patenting frequency may increase or decrease for all firms. To control

for such time-varying effects, we included year fixed effects for each year, with 2000

being the reference year.

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4. ESTIMATION

As the dependent variable of this study, the number of patents applied for and received by

firms, is a count variable taking only non-negative integer values, we employ various

count panel data models—the multiplicative distributed lag model and the dynamic linear

feedback model—to investigate the relationship between patenting and internal R&D

activity of firms in the global pharmaceutical industry. For simplicity, all estimation

methods to be used in our empirical analysis will only be sketched here. The relevant

models and the associated moment conditions to be solved are described in Appendix B

(See GMM І and PSM І for the estimation of Model (1), the multiplicative distributed lag

model, and GMM II and PSM II for estimating Model (2), the dynamic linear feedback

model).

4.1 Multiplicative Distributed Lag Model

The conditional mean for a standard multiplicative distributed lag model is specified as

E ¿¿

¿exp( β0+β1 logRD¿+…+βτ +1logRD ¿−τ+s i' θi+wt

' θt +ηi) (1)

where p¿ are the number of patents applied for and received by firm i in period t, RD¿

denotes annual R&D expenditures, si is a vector of observable firm-specific effects (such

as firm size, firm nationality, and Pharma firm)14, w t is a vector of time-specific variables

(i.e., year fixed effects), and ηi represents unobserved individual fixed effects, which are

commonly modeled multiplicatively in count panel data models.

14 The firm-specific effects siare only included in the random-effects specifications. 16

The basic reference for estimating the above model is the Poisson and negative

binomial estimations (Hausman et al., 1984). Both random- and fixed-effects

specifications are used in this study to control for unobserved individual fixed effects, ηi,

in the Poisson and negative binomial estimations. The problem with the random

(uncorrelated) effects formulation is that it is inconsistent when ηi is correlated with the

regressors of interest15. Conditional fixed-effects specification, however, allows for such

correlations (Hall et al., 1986; Hausman et al., 1984). It is also important to note that, on

account of the overdispersed nature of patent counts, the negative binomial estimation

provides a better fit for our data than the Poisson estimation since the assumption of the

equality of conditional mean and conditional variance may not hold (Hall et al., 1986;

Hausman et al., 1984).

The consistency of the standard estimators presented above relies on the strict

exogeneity of the explanatory variables. As previously discussed, new patents may

depend on additional R&D expenditures in the future for their full development, the

series of current and lagged R&D expenditures is therefore weakly exogenous or

predetermined in our estimation models. As an alternative to the standard estimators,

Chamberlain (1992) and Wooldridge (1997) have proposed a quasi-differenced GMM

estimator that relaxes the strict exogeneity assumption. Specifically, they provide a

transformation strategy that eliminates the unobserved fixed effects and then use valid

moment conditions to obtain consistent estimation. In this study, we follow Wooldridge’s

15 There are reasons to believe that in many circumstances such correlations may exist. For instance, firms that have a higher propensity to patent for unobserved reasons may invest more in R&D as the return from R&D is higher than that from other investment projects (Montalvo, 1997).

17

(1997) quasi-differencing transformation and use the instruments¿) as below, which

require a restricted serial correlation of the residuals16.

z¿=(1 , log RD¿−(τ +1) , …, log RDi 1 , p¿−(τ +2 ) , …, p i1 , w t' )

On the other hand, the GMM estimator is subject to some problems, namely small

sample bias and imprecision when the series are highly persistent, as the instruments are

then weak predictors of the endogenous changes (Blundell et al, 1995; Blundell et al.,

2002). As an alternative, Blundell et al. (2002) propose a pre-sample mean (PSM)

estimator that replaces the unobserved fixed effect by the pre-sample mean of the

dependent variable. In view of the highly persistent R&D series of this study, as will be

exhibited in Table 2, we used the PSM estimator as well.

4.2 Dynamic Linear Feedback Model

An additional complication to the highly persistent R&D series is that the current and

lagged R&D terms in the multiplicative distributed lag model [i.e., Model (1)] are

collinear. To solve this problem, Blundell et al. (2002) develop a dynamic linear

feedback model by explicitly introducing the dynamics of the count process in panel data.

In contrast with Model (1), in the dynamic linear feedback model, the lagged dependent

variable enters the conditional mean specification linearly, which corresponds to the

following17

16 The GMM estimation is inconsistent if the requirement on the instruments ( z¿) is not satisfied (See Crépon and Duguet, 1997). Alternatively, S¿=(1 , log RD¿−( τ+1 ) , log RD¿−( τ+2 ) , …, log RD i1 , w t

' ) can be used as the instruments, which do not require a restricted serial correlation of the residuals. The difference between these two sets of instruments is that the latter could lose efficiency in the presence of a restricted serial correlation of the residuals. We used S¿ as well and the estimation results were basically similar. 17 Blundell et al. (2002) argue that inclusion of functions of the lagged dependent variable in the exponential function can lead to explosive series for patents or cause problems with transforming zero

18

E ¿¿ (2)

where (1−γ ) estimates the depreciation factor, α 1 and (1−γ )α1 are the long-run and

short-run elasticities of patents with respect to internal R&D, respectively (See Appendix

B for an economic interpretation of the dynamic linear feedback model).

Following Blundell et al. (2002), we use two approaches to obtaining estimates for

the dynamic linear feedback model [i.e., Model (2)]. The first is the GMM estimator,

based on a quasi-differencing transformation proposed by Wooldridge (1997) and a

choice of the instruments as follows:

z¿=(1 , log RD¿−1 , log RD¿−2 , …, log RD i 1 , p¿−2 , …, p i 1 , w t' )

A further estimation of Model (2) using the PSM estimator, as discussed earlier, includes

pre-sample information on the number of patents to control for individual fixed effects.

Both estimators are consistent in the presence of predetermined regressors and correlated

fixed effects.

5. RESULTS

The main findings for Model (1), in which five lagged R&D terms are included18, and

Model (2) are presented in Table 3. Columns 1 through 4 give results from the standard

Poisson and negative binomial estimations of Model (1). The coefficients on

contemporaneous and the first lag (t - 1) of R&D are positive and significant across all

the Poisson and negative binomial regression models. Moreover, a consistent pattern of a

U-shaped lag structure is found, with the first (t) and last (t - 5) coefficients being larger

values.18 Following Hausman et al. (1984) and Pakes and Griliches (1984a), the multiplicative distributed lag model [i.e., Model (1)] is constructed with five lagged R&D terms.

19

than those in the middle, for the Poisson and negative binomial models in both the

random- and fixed-effects specifications.

The significant, positive, and large coefficient on the last lag (t-5) of R&D could be

due to the correlation of the last R&D variable with earlier left-out R&D. If this is the

case, a U-shaped lag structure is solid evidence for a lag truncation effect in the

distributed lag of R&D on patents (Hall et al., 1986; Pakes and Griliches, 1984a). To

explore this idea further, we performed autoregressive regressions on the R&D series. As

shown in Table A1 (see Appendix A), an AR (2) process can be accepted at 5%

significance level. Nonetheless, the first lag coefficients are close to one and the second

lag coefficients are relatively small, which implies that it is difficult to reject a random

walk process. Hence, the R&D series of this study conforms to a random walk or an AR

(2) process and suggests the existence of a lag truncation effect.

On the other hand, the fairly large coefficient on the last lagged R&D may also be

caused by correlated fixed effects, i.e., the correlation between the permanent patenting

propensity of firms and their investments in internal R&D (Hall et al., 1986; Pakes and

Griliches, 1984a). We then used fixed-effects models that allow for such correlations, and

a U-shaped lag structure was identified as well in the fixed effects formulation. This

finding suggests that correlated fixed effects do not bias the estimated results and there is

indeed a lag truncation effect in the distributed lag relationship between patenting and

R&D expenditures. By contrast, previous work is inconclusive about the lag structure of

the patents-R&D relationship. Hausman et al. (1984) and Hall et al. (1986) found a U-

shaped lag structure for the Poisson and negative binomial random-effects models, but

only a contemporaneous relationship was identified in their conditional fixed-effects

20

models. In the recent study by Gurmu and Pérez-Sebastián (2008), a U-shaped lag

structure was found for the random- and fixed-effects Poisson models but no evidence of

it in the case of negative binomial models.

Insert Table 3 here

Results for Model (1) using the less constrained GMM and PSM estimators, which

relax the strict exogeneity assumption, are reported in columns GMM І and PSM І,

respectively (see Table 3 Continued)19. In the GMM estimation, a Sargan Difference test

is used to check for overidentifying restrictions, and m1 and m2 are tests for first- and

second-order serial correlation. As shown in column GMM І, the Sargan test does not

reject the null hypothesis that the additional moment conditions are valid. In addition, the

first- and second-order serial correlation tests are consistent with the serially uncorrelated

error term (i.e., significant m1 and insignificant m2). The specification tests thus do not

indicate misspecification in GMM І. Comparison of the results from GMM І to those

from the Poisson and negative binomial estimations shows that there are still strong

contemporaneous and lag effects of R&D, with significant positive coefficients on t, t-1,

and t-5. However, a negative and significant effect is found at the second lag (t-2) of

R&D. Although this is not as expected, similar cases also occur in previous studies (see

Gurmu and Pérez-Sebastián, 2008; Montalvo, 1997)20. The puzzling estimated form of

19 Our thanks go to Frank Windmeijer for his Gauss program, EXPEND, to estimate Model (1) and (2) using the GMM and PSM estimators (see Windmeijer, 2002).20 In Montalvo (1997), the estimated coefficient on contemporaneous R&D was barely different from zero, whereas the first lag of R&D was positive and significant. Likewise, puzzling results were also found in the study by Gurrmu and Pérez-Sebastián (2008), where a negative and significant effect was identified at the fourth lag of R&D.

21

the lag structure in GMM І possibly arises from a problem of weak instruments, as the

R&D series in our data set is highly persistent over time (the first order autocorrelation is

about 0.99 as displayed in Table 2) and the instruments are only weakly correlated with

the endogenous variables in the differenced model (Bond and Windmeijer, 2005;

Blundell et al, 1995; Blundell et al., 2002).

In column PSM І, results are given from the PSM estimator for the estimation of

Model (1). The pre-sample mean of patents is positive and statistically significant,

indicating that it is important to control for the unobserved differences in the capabilities

for knowledge production with which firms entered the sample. With regard to the

influence of internal R&D, both the contemporaneous and first lagged R&D terms retain

their signs, though with reduced level of significance. The significant effect of the last lag

of R&D, however, no longer appears in the PSM І version. The explanation lies in the

fact that the information contained in the pre-sample mean becomes close to that reflected

by the R&D series when the R&D process is highly persistent. Thus, the separate

estimation of the parameters on R&D and the pre-sample mean is problematic due to

multicollinearity (Blundell et al., 2002). Since the variance of the fixed effect (proxied by

the pre-sample mean) is relatively large, the parameter on the pre-sample mean variable

will get a larger weight, leading to a downward bias in the parameters for R&D series21.

To give a brief summary of Model (1), based on the various estimations presented

above, in all cases the results suggest that there are lag effects of internal R&D as well as

a significant contemporaneous relationship between patents and R&D. Consistent with

21 See Blundell et al. (2002), the PSM estimator performs better in Monte-Carlo simulations in comparison to the GMM estimator. However, there is an increase in the bias and root mean squared error for the PSM estimator of β when the R&D series becomes very persistent.

22

prior literature, the impact of contemporaneous R&D on patents is rather strong.

Nonetheless, our study differs substantively from previous work in that the estimation

results exhibit direct evidence on lagged R&D effects, with the first lag of R&D being

significant in all distributed lag specifications. More importantly, a U-shaped lag

structure of the patents-R&D relationship is identified across the various estimations of

Model (1) (except for PSM І), suggesting a potential long-run effect of internal R&D

investments on firm patenting.

We now turn to the estimation of Model (2), the dynamic linear feedback model,

which essentially allows for the dynamics of the count process itself. Results for Model

(2) using the GMM and PSM estimators are reported in columns GMM II and PSM II,

respectively (see Table 3 Continued). As seen in GMM II, the specification tests provide

no evidence against the model. The estimated coefficients on the lagged dependent

variable and R&D equal to 0.21 (γ ) and 0.73 (α 1¿. This implies that the contribution of

internal R&D investments depreciates exponentially at the rate of approximately (1−γ ) =

79%, with the short-run elasticity of patents with respect to R&D of about (1−γ )α1 =

0.57 and the long-run elasticity of about α 1 = 0.73. These results provide an indication of

lag effects of R&D expenditures on patents, though at a relatively fast moving process.

The suspicion is still that, as in the case of GMM І, the GMM estimator is subject to

small sample bias and the weak instrument problem, particularly when R&D series is

highly persistent over time (Blundell et al, 1995; Blundell et al., 2002).

The estimates from PSM II show a rather different picture, with a fairly low

depreciation rate of approximately 10% and the long-run elasticity of patents with respect

to R&D of about 0.50, which is substantially larger than the short-run elasticity, 0.05.

23

Therefore, PSM II implies a much slower moving process and accordingly an overall

long-run effect of in-house R&D on firm patenting. In this vein, the estimation results

from Model (2), the dynamic linear feedback model, coincide with those from Model (1),

the multiplicative distributed lag model, indicating not only lag effects but also a

potential long-run effect of internal R&D investments in a firm’s knowledge production

and innovation process.

Insert Table 3 Continued here

6. DISCUSSION AND CONCLUSIONS

The principal purpose of this study is to revisit the classic research question of the lag

structure of the patents-R&D relationship through an examination of the impact of

internal R&D on firm patenting in the context of the global pharmaceutical industry

during 1986–200022. Our empirical analysis shows that, although our results are

somewhat sensitive to different estimation methods, the total elasticity of patenting with

respect to R&D varies from 0.3 to 0.9, indicating decreasing returns to scale in internal

R&D. Consistent with prior research, the impact of contemporaneous R&D on patents is

22 We acknowledge that a firm’s knowledge production and innovation could arise from both its internal and external R&D investments. The focus in our paper is on the role of internal R&D as a basis for sustainable innovative capabilities of firms. The impacts of external R&D such as R&D alliances and acquisitions are beyond the scope of this study. As a robustness test, we also ran all the model estimations by including a firm’s external R&D investments, through R&D alliances and R&D acquisitions. R&D alliances are measured as the number of alliances between incumbent pharmaceutical firms and new biotechnology companies, in which a combined innovative activity or an exchange of technology is invloved. Likewise, R&D acquisitions are measured as the number of acquisitions undertaken by incumbent pharmaceuticals, which targetted new biotechnology companies for their R&D capabilities. A one-year lag was employed on both variables to alleviate a potential simultaneity bias. We found that the inclusion of external R&D does not alter the estimation results, including the lagged R&D effects and the U-shaped lag structure of the patents-R&D relationship, across the various estimations of model (1) and model (2). An exception is GMM І, in which the Sargan test rejects the null hypothesis and indicates that the model is misspecified.

24

rather strong, accounting for over 36% of the overall R&D elasticity. However, our study

differs from previous work that examines the patents-R&D relationship in three aspects.

First, our estimation results exhibit direct evidence on lagged R&D effects, with the first

lag (t-1) of R&D being significant in all distributed lag specifications. Evidence for the

contribution of the first lag of R&D to the current year’s patent counts is of more than

25% of the total R&D elasticity. Second, a U-shaped lag structure of the patents-R&D

relationship is identified across the various estimations of the multiplicative distributed

lag model (except for PSM І). This finding suggests a potential long-run effect of internal

R&D investments on firm patenting. Finally, the estimation results for the dynamic linear

feedback model, especially from the PSM estimator, coincide with those from the

multiplicative distributed lag model, with a fairly low depreciation rate of approximately

10% of internal R&D investments over time and accordingly an overall long-run effect of

internal R&D on firm patenting. In short, our empirical findings, from both the

multiplicative distributed lag model and the dynamic linear feedback model, provide

evidence for not only lag effects from recent R&D investments but, in support of our

main hypothesis, also a potential long-run effect of internal R&D investments on the

distant past in the knowledge production or innovation process of incumbent

pharmaceutical firms.

To summarize, our results illustrate a cumulative knowledge production or

innovation process of incumbent pharmaceutical firms, with current patent production

being historically dependent on past investments in internal R&D. These results are

consistent with prior research which suggests that not only recent knowledge is important

for new knowledge creation, but that older knowledge in knowledge stock accruing from

25

long past R&D investments may also be valuable for firm innovativeness (Katila, 2002;

Nerkar, 2003). This finding echoes the real options logic for managing R&D investment

strategies of firms (McGrath, 1997; McGrath and Nerkar, 2004), according to which early

R&D investments by firms in a new area with technical uncertainty may be influential in

their knowledge production or innovation process over a long-term horizon. After the

initial investment in R&D, firms can choose to wait until conditions favor the (re)use of

the old untapped knowledge (McGrath, 1997; Nerkar, 2003). Alternatively, firms may opt

for making further R&D investments in the same area in a sequential way, which

enhances the value of the initial R&D investment and makes it valuable for future

innovation.

From a managerial perspective, our study offers important insights into the

cumulative knowledge production or innovation process of firms. In addition to

emphasizing recent investments in internal R&D to stay abreast of the latest, cutting edge

technologies, decision-makers in firms should also adopt a long-term perspective for

organizing R&D investment strategies. Through periodically reviewing and recombining

the old, useful but under-utilized knowledge, firms can increase their creation of new

knowledge (Garud and Nayyar, 1994; Nerkar, 2003). However, it is worth to note that old

knowledge tends to be lost over time due to lack of adequate organizational memory,

inaccurate recording, and turnover in R&D personnel (Argote, 1999). As a consequence,

to effectively transfer knowledge across time, firms need to build up their ‘transformative

capacity’, which pertains to the choice of knowledge for future use, its maintenance over

time, and the reactivation and synthesis of such knowledge when required (Garud and

Nayyar, 1994). In this way, by making better use of old knowledge and actively

26

maintaining stock of knowledge for future use, firms can enhance their returns from

internal R&D investments.

Our study is subject to some limitations which suggest avenues for future research.

The restriction of the sample to a single industrial context raises the question of the

generalizability of our findings, thus further efforts could be made to conduct research in

other high-technology industries. In addition, as the proportion of research (‘R’) in R&D

expenditures is the main contributor to patents (Czarnitzki et al., 2009; Griliches, 1990),

future work directed towards a fine-grained analysis of disaggreating ‘R’ and ‘D’ would

contribute to a better understanding of the overall lag structure of the patents-R&D

relationship.

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Table 1 Descriptive Statistics

Variable Mean S. D. Min Max

R&D Expenditures* 504.75 587.83 1.51 2767.50

Number of patents 94.11 128.95 0 800

First quartile number of patents 14

Median number of patents 45

Third quartile number of patents 116

Fraction with zero patents 0.01

Fraction with at least 100 patents 0.29

Pre-sample Mean 69.30 91.76 0.10 362.80

Equity** 4720.16 4825.73 7.08 17507.77

European Firm 0.30 0.46 0 1

US Firm 0.33 0.47 0 1

Pharma Firm 0.46 0.50 0 1

Note: * R&D Expenditures are inflation-adjusted in millions of year 2000 dollars. ** We used the logarithm of book value of equity in year 2000 in millions of dollars, as a time-constant variable, to proxy for firm size. For those firms that fail to survive till year 2000, the end year value of equity is used and inflation-adjusted.

Table 2 Correlation Matrix

Patentst Log R&Dt Log R&Dt-1 Log R&Dt-2 Log R&Dt-3 Log R&Dt-4

Log R&Dt 0.6101

Log R&Dt-1 0.6167 0.9933

Log R&Dt-2 0.6217 0.9839 0.9930

Log R&Dt-3 0.6273 0.9749 0.9838 0.9933

Log R&Dt-4 0.6299 0.9651 0.9749 0.9847 0.9934

Log R&Dt-5 0.6318 0.9504 0.9624 0.9740 0.9826 0.9922

32

Table 3 Estimates of the Knowledge Production Function from Patent Numbers

Variable Poisson(random-effects)

Poisson(fixed-effects)

Negative Binomial (random-effects)

Negative Binomial(fixed-effects)

Constant -0.0403(0.5779)

0.0048(0.3967)

-0.5668*

(0.2717)Year Dummies Included Included Included Included

European Firm -0.0164(0.2054)

-0.3471*

(0.1527)US Firm 0.7599***

(0.2000) 0.1390(0.1584)

Pharma Firm -0.6679***

(0.1700)-0.5137***

(0.1187)Log Equity -0.1412†

(0.0764)-0.1523*

(0.0621)Log R&D t 0.3654***

(0.0362) 0.3813***

(0.0363) 0.2517**

(0.0943) 0.2392*

(0.1028)Log R&Dt-1 0.2493***

(0.0500) 0.2449***

(0.0499) 0.2937*

(0.1330) 0.2432†

(0.1415)Log R&Dt-2 0.0365

(0.0533) 0.0445(0.0533)

-0.0164(0.1383)

-0.0416(0.1464)

Log R&Dt-3 0.1122*

(0.0536) 0.1154*

(0.0536) 0.0578(0.1379)

-0.0223(0.1439)

Log R&Dt-4 -0.0522(0.0516)

-0.0493(0.0516)

-0.0948(0.1325)

-0.0854(0.1374)

Log R&Dt-5 0.2383***

(0.0372) 0.2520***

(0.0373) 0.2080*

(0.0934) 0.1926*

(0.0956)Sum ofR&D Elasticity 0.9495 0.9888 0.7000 0.5257

Log Likelihood -4498.0885 -3888.3712 -3327.3603 -2713.6075

Chi Square 2339.20*** 2212.43*** 368.04*** 226.49***

33

Table 3 Continued

Variable GMM І

PSM І

GMM II

PSM II

Constant 3.7630***

(0.1001) 1.7962***

(0.3536)Year Dummies Included Included Included

Log Pre-sample Mean 0.6121***

(0.0660) 0.3797**

(0.1383)Patent t-1 0.2130***

(0.0172) 0.9003***

(0.0439)Log R&D t 0.4443***

(0.0629) 0.3058†

(0.1583) 0.7276***

(0.0315) 0.4995**

(0.1529)Log R&Dt-1 0.2664***

(0.0703) 0.1646†

(0.0981)Log R&Dt-2 -0.2992***

(0.0884) -0.0866(0.1393)

Log R&Dt-3 0.0248(0.0734)

0.1394(0.1224)

Log R&Dt-4 0.1140(0.0699)

-0.1456(0.0940)

Log R&Dt-5 0.1698*

(0.0683)-0.0707(0.1611)

Sum ofR&D Elasticity 0.7201 0.3069

Sargan [p-value] 55.5390[0.1139] 69.0116[0.1991]

m1[p-value] -2.5497[0.0108] -4.0400[0.0001]

m2 [p-value] -1.2863[0.1983] 0.0049[0.9961]

Notes: 1. Standard errors are in parentheses. Year dummies are included but not shown, except for in PSM (II)

estimation, for which we could not achieve convergence with the inclusion of fixed year effects.2. † p<0.10, * p<0.05, ** p<0.01, *** p<0.001.3. N = 1,186 firm-year observations, the study has a slightly unbalanced panel sample of 85 firms covering the

period from 1986 to 2000. 4. GMM (І) and PSM (І) provide estimates for Model (1), the multiplicative distributed lag model; GMM (II)

and PSM (II) provide estimates for Model (2), the dynamic linear feedback model. 5. The diagnostic tests for GMM (I) and GMM (II) include: Sargan = the Sargan test for overidentifying

restrictions, m1 = first-order serial correlation, m2 = second-order serial correlation; p-values are in brackets.

34

APPENDIX ATable A1 Autoregressive Estimates for Log R&Dt

Equation (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)

Log R&Dt-1 0.993***

(0.005) 1.158***

(0.044) 1.144***

(0.049) 1.152***

(0.049) 1.175***

(0.051) 1.154***

(0.044) 1.147***

(0.045) 1.130***

(0.046) 1.138***

(0.048) 1.170***

(0.049) 1.154***

(0.045) 1.140***

(0.047) 1.151***

(0.048) 1.180***

(0.049)Log R&Dt-2 -0.161***

(0.045)-0.122(0.076)

-0.126(0.077)

-0.168*

(0.077)-0.161***

(0.046)-0.152**

(0.047)-0.129**

(0.048)-0.140**

(0.049)-0.173**

(0.050)-0.157**

(0.047)-0.137**

(0.048)-0.151**

(0.049)-0.181***

(0.050)Log R&Dt-3 -0.022

(0.041) 0.061(0.071)

0.029(0.076)

Log R&Dt-4 -0.093(0.055)

0.043(0.087)

Log R&Dt-5 -0.081(0.056)

Log Patentt 0.027*

(0.012) 0.034*

(0.014) 0.036*

(0.015) 0.039**

(0.014) 0.030**

(0.011)Log Patentt-1 -0.022

(0.012)-0.004(0.013)

-0.000(0.014)

-0.004(0.014)

-0.008(0.014)

0.018(0.013)

0.022(0.015)

0.019(0.015)

0.009(0.014)

Log Patentt-2 -0.028(0.015)

-0.015(0.018)

-0.008(0.019)

-0.002(0.019)

-0.018(0.013)

-0.006(0.017)

0.000(0.019)

0.004(0.019)

Log Patentt-3 -0.021(0.014)

-0.020(0.015)

-0.015(0.017)

-0.018(0.013)

-0.019(0.015)

-0.013(0.017)

Log Patentt-4 -0.009(0.012)

-0.005(0.016)

-0.005(0.012)

-0.000(0.016)

Log Patentt-5 0.002(0.015)

-0.001(0.015)

R2 0.987 0.988 0.988 0.988 0.989 0.988 0.988 0.988 0.989 0.989 0.988 0.988 0.988 0.989

Notes: 1. All equations contain a separate intercept for each year.2. Due to the presence of zero values, we added 1/3 to the patents variable before taking the logarithms. 3. Standard errors shown in parentheses are heteroskedastic-consistent estimates.4. * p<0.05, ** p<0.01, *** p<0.001.

35

APPENDIX B

1. Multiplicative Distributed Lag Model [Model (1)]

The conditional mean for a standard multiplicative distributed lag model for count panel data

is of the form23:

E ( y¿|X ¿ , ηi )=exp ( X¿' β+ηi )=μ¿ ν i (B1)

whereμ¿=exp ( X ¿' β ), and νi=exp (ηi ) is a permanent scaling factor for the individual specific

mean.

In the present study, the innovation model is written as,

X ¿' β=β0+β1 x¿+β2 x¿−1+…+βτ +1 x¿−τ+control' θ (B2)

where y¿ are the number of patents applied for and received by firm i in period t (i = 1, …, N;

t = 1, …, T),x¿ denotes the natural logarithm of annual R&D expenditures, andcontrol is a

vector of control variables.

GMM І

In this study the generalized method of moment (GMM) estimator applies the Wooldridge’s

(1997) quasi-differencing transformation24:

q¿=y¿

μ¿−

y¿−1

μ¿−1. (B3)

When x¿ , x¿−1 , …, x¿−τ are predetermined, the following moment conditions hold25,

E (q¿∨x i 1 , x i 2 ,…, x¿−1 )=0. (B4)

23 The Cobb-Douglas knowledge production function is applied in this model.24 An alternative is the Chamberlain (1992) quasi-differencing transformation:

s¿= y¿

μ¿−1

μ¿− y¿−1.

25 z¿=(1 , x¿−(s+1) , x¿− (s+2) ,… , x i 1 ,control' ) is used as the instruments, where s ( s = 0, …,τ ) represents the

extent to which the z¿ are weakly exogenous, i.e., s = 0 (s = 1, …,τ ) means thatx¿−1(x¿−2 , …,x¿− ( τ+1)) in thez¿ (Cincera, 1997).

36

PSM І

The pre-sample mean (PSM) estimator solves the following moment conditions when

estimating the multiplicative distributed lag model:

∑i=1

N

∑t=τ +1

T

z¿( y¿−exp (β0¿+β1 x¿+…+ β τ+1 x¿−τ+control' θ+ϕlog y ip ))=0(B5)

where y ip=1

TP ∑r=0

TP−1

y i 0−r is the pre-sample mean of y, TP is the number of pre-sample

observations, and z¿=(1 , x¿ , x¿−1 , …,x¿−τ , control' , log y ip).

2. Dynamic Linear Feedback Model26 [Model (2)]

Dynamic linear feedback model in the patents-R&D relationship: An economic interpretation

Instead of using Cobb-Douglas knowledge production function, R&D expenditures are

combined through a specific parameterization of the CES knowledge production function to

produce knowledge stock:

Q¿=k (RD¿β+(1−δ ) RD¿−1

β +…)ψ /β v i (B6)

where Q¿ is some latent measure of technological output of firm i in period t, k is a positive

constant, R&D investment depreciates exponentially at rate δ , and vi captures the firm

specific propensity to patents.

As observed patents are a noisy indicator of a firm’s technological output, we write

p¿=Q¿+ε¿ (B7)

26 See Blundell et al. (2002). 37

where p¿ are the number of patents applied for and received by firm i in period t, and

E (ε ¿|RD¿ , RD¿−1 ,…, v i )=0.

Setting the returns to scale parameter ψ equal to β in (B6) and using (B7) results in,

p¿=k (RD¿β+(1−δ ) RD¿−1

β +…)v i+ε¿. (B8)

Ignoring any feedback from patents to R&D expenditures, the long run steady state for firm i

may be written as

pi=kδ

RDiβ vi (B9)

thus β may be interpreted as the long run elasticity of patents with respect to R&D, and δ∗β

is the short run elasticity.

Inverting (B8) results in,

p¿=(1−δ ) p¿−1+k RD¿β vi+u¿ (B10)

= (1−δ ) p¿−1+exp ¿

with E (u¿|p¿−1 , RD¿ , v i )=0.

From (B10), the conditional mean in the dynamic linear feedback model is defined as,

E( y¿¿¿∨ y¿−1 , X ¿ , v i)=γ y¿−1+exp¿¿ (B11)

where

X ¿' α=α 0+α1 x¿+control' θ

γ=1−δ

α 1=β

38

y¿ are the number of patents applied for and received by firm i in period t (i = 1, …, N; t = 1,

…, T),x¿ denotes the natural logarithm of annual R&D expenditures, andcontrol is a vector of

control variables.

GMM II

In this study the generalized method of moment (GMM) estimator applies the Wooldridge’s

(1997) quasi-differencing transformation27:

q¿=y¿−γ y¿−1

μ¿−

y¿−1−γ y¿−2

μ¿−1(B 12)

When x¿is predetermined, the following moment conditions hold

E (q¿∨ y i1 , y i2 , …, y¿−2 , x i 1 , x i 2 , …, x¿−1 )=0. (B13)

PSM II

The pre-sample mean (PSM) estimator solves the following moment conditions when

estimating the dynamic linear feedback model:

∑i=1

N

∑t=2

T

z¿ ( y¿−γ y¿−1−exp (α0¿+α1 x¿+control' θ+ϕlog yip ))=0(B 14)

where y ip=1

TP ∑r=0

TP−1

y i 0−r is the pre-sample mean of y, TP is the number of pre-sample

observations, and z¿=(1 , y¿−1 , x¿ , control' , log y ip ).

27 An alternative is the Chamberlain’s (1992) quasi-differencing transformation as follows:

s¿=( y¿¿¿−γy¿−1)μ¿−1

μ¿−( y¿¿¿−1−γy¿−2)¿¿.

39